Here in NYC the Metropolitan Transit Authority (subway, buses, regional commuter rail, bridges and tunnels - anything you pay a fare or toll for) had a 2013 budget (PDF) of $1,357,806,000. And that's still bleeding damn near another billion a year, with 25% fare increases and 25% service cuts. You could probably slash that overrrun quite a bit more by stopping all current and planned construction/improvements and going to a minimal-maintenance schedule, good luck with that.
Yeah, free transit is a great idea in theory, but if you've figured out how to squeeze three billion dollars a year in sustainable tax revenue out of a single city, even a large one, you're a better economist than I.
Clue this: the homeless have pretty much free access to the subways - most stations no longer have attendants on duty so hopping a turnstile and riding for days on end is feasible. Hell, I've done it myself (I have a monthly pass so not swiping isn't taking a fare). Foul smelling, insane homeless emptying entire train cars is a bigger problem than them freezing to death, at least in this town.